Nikola Kalinic's second goal in Spain's top flight – courtesy of a wonderful Griezmann pass – was followed by his strike partner's 124th – the points appearing safe when he converted from the penalty spot on the stroke of half-time.
But Atletico's defensive solidity uncharacteristically failed and Saul Niguez's own goal after Fernando Calero's header meant it was all square in the 63rd minute.
It was left to Griezmann to punish a scuffed Oscar Plano clearance 10 minutes from time and move Diego Simeone's side level on points with Barcelona at the summit.
Valladolid started in impressive fashion, taking the game to Atletico and starving its creative players of space.
But Griezmann found a pocket in which to operate in the 26th minute and Kalinic was on hand to stroke home his team-mates' sumptuous throughball.
Plano and Enes Unal passed up clear chances for the host as Atleti showed unusual vulnerability down its right flank and Valladolid was made to pay with the final action of the half.
Jordi Masip saved brilliantly from Griezmann's deflected shot before a VAR review showed the deviation came courtesy of Kiko Olivas' handball, and the France star clinically dispatched the penalty.
As in the opening period, Valladolid resumed on the front foot and its pressure told in the 57th minute.
Calero rose highest to power captain Michel's corner past the efforts of Jan Oblak and Santiago Arias on the line.
Sergio Gonzalez's men were ruthless in seizing upon an unusually vulnerable Atletico and they were level when Saul diverted Unal's header from a right-wing corner into the net.
But having caused Atleti repeated problems from set-pieces, Valladolid faltered in deflecting one and Griezmann needed no second invitation to thump into the bottom corner.